HEURISTIC APPROACHES FOR SOLVING HUB LOCATION PROBLEM 劉曉君、吳泰熙,蕭育如
E-mail: 9018612@mail.dyu.edu.tw
ABSTRACT
THE LOCATION OF HUB FACILITIES IS FUNDAMENTAL TO THE DESIGN OF A "HUB-AND-SPOKE NETWORK", AS IT GREATLY AFFECTS THE TOTAL TRANSPORTATION COSTS OF SYSTEM. HUB IS A SPECIAL TYPE OF FACILITY, WHICH IS DESIGNED TO ACT AS SWITCHING POINT FOR INTERNAL FLOWS OF A NETWORK. THE PROBLEM IS TO DETERMINE THE OPTIMAL LOCATION FOR THE HUBS AND THE ASSIGNMENTS OF THE NONHUBS TO HUBS THAT MINIMIZES THE OVERALL TRANSPORTATION COST. DUE TO ITS
CHARACTERISTICS OF NP-COMPLETE, IT IS DIFFICULT TO OBTAIN OPTIMAL SOLUTION WITHIN AN
ACCEPTABLE AMOUNT OF TIME. IN THIS STUDY WE CONSIDER BOTH SINGLE AND MULTIPLE ALLOCATION HUB LOCATION PROBLEMS. A HEURISTIC ALGORITHM BASED ON A HYBRID OF SIMULATED ANNEALING (SA) AND TABU LIST IS DEVELOPED. BESIDES, A LAGRANGIAN RELAXATION APPROACH IS ALSO PRESENTED TO SOLVE THIS PROBLEM. BOTH HEURISTIC APPROACHES PRESENTED IN THIS STUDY COMPARE
FAVORABLY WITH THE COMPUTATIONAL RESULTS OBTAINED FROM THE LITERATURE. THE RESULTS INDICATE THAT BOTH METHODS PROPOSED ARE CAPABLE OF OBTAINING GOOD SOLUTIONS IN A VERY SMALL AMOUNT OF TIME.
Keywords : HUB LOCATION PROBLEM, SIMULATED ANNEALING, LAGRANGIAN RELAXATION Table of Contents
第一章 緒 論--P1 1.1 研究背景與動機--P1 1.2 研究目的--P3 1.3 研究範圍與限制--P3 1.4 研究流程--P4 第二章 文獻探討--P7 2.1 轉接點位址問題之發展--P7 2.2 相關研究整理--P10 2.2.1 延伸題型--P11 2.2.2 其他相關研究--P12 2.3 啟發式方法--P14 2.3.1 模擬退火法--P15 2.3.2 禁忌搜尋法--P19 第三章 轉接點問題之求解--P23 3.1 問題定義--P23 3.1.1 單一分派問題--P24 3.1.2 多重分派問題--P26 3.2 SAHUB演算法--P27 3.2.1 起始解--P28 3.2.2 移步策略--P30 3.2.3 SA參數及禁忌名單長度--P35 3.2.4 收斂準則--P37 3.2.5 轉接點位址問題SAHUB演算法之建立--P37 3.3 拉氏鬆弛法--P41 3.3.1 拉氏鬆弛模式--P42 3.3.2 轉 接點位址問題拉氏鬆弛演算法之建立--P43 3.3.3 建構可行解--P44 3.3.4 參數說明--P46 3.3.5 演算停止法則--P47 第四章 結果 分析--P48 4.1 文獻例題介紹--P48 4.2 單一分派例題測試結果與分析--P49 4.3 多重分派例題測試結果與分析--P52 第五章 結 論--P56 5.1 研究總結--P56 5.2 未來研究建議--P57 【 參考文獻 】--P58 附錄一--P66 附錄二--P70 附錄三--P72 附錄四--P74 附 錄五--P76
REFERENCES
[ 1]熊正一，"兩岸空運直航航點選擇策略之研究"，國立成功大學碩士論文，民國88年六月。
[ 2]林正章，"兩岸直航航線選擇使用者均衡模式之研究"，民航季刊，民國88年。
[ 3]林正章、劉志遠， "兩岸直航航線選擇使用者均衡模式之研究" ，民航季刊，1(2)，197-218，1999。
[ 4]許巧鶯、王志青，"軸輻航空貨運網路之直接與轉運路線選擇"，運輸計劃季刊，26(1)，95-118， 1997。
[ 5]張斐茹，"軸輻路網在國際定期貨櫃船航線之應用"，國立交通大學交通運輸研究所碩士論文，民國 98年。
[ 6]ABDINNOUR-HELM SUE, "A HYBRID HEURISTIC FOR THE UNCAPACITATED HUB LOCATION PROBLEM," EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 106, 489-499, 1998.
[ 7]ANANTARAM BALAKRISHNAN, THOMAS L. MAGNANTI AND PRAKASH MIRCHANDANI, "MODELING AND HEUR ISTIC WORST-CASE PERFORMANCE ANALYSIS OF THE TWO-LEVEL NETWORK DESIGN PROBLEM," MANAGE -MENT SCIENCE, 40(7), 486-867, 1994.
[ 8]ANDREAS T. ERNST AND MOHAN KRISHNAMOORTHY, "AN EXACT SOLUTION APPROACH BASED ON SHORTE -ST-PATHS FOR P-HUB MEDIAN PROBLEMS," INFORMS JOURNAL ON COMPUTING, 10(2), 149-162, 1998.
[ 9]ANDREAS T. ERNST AND MOHAN KRISHNAMOORTHY, "EFFICIENT ALGORITHMS FOR THE UNCAPACITATED SINGLE ALLOCATION P-HUB MEDIAN PROBLEM," LOCATION SCIENCE, 4(3), 139-154, 1996.
[10]ANDREAS T. ERNST AND MOHAN KRISHNAMOORTHY, "EXACT AND HEURISTIC ALGORITHMS FOR THE UNC
-APACITATED MULTIPLE ALLOCATION P-HUB MEDIAN PROBLEM," EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 104, 100-112, 1998.
[11]AYKIN TURGUT, "LARGRANGIAN RELAXATION BASED APPROACHES TO CAPACITATED HUB-AND-SPOKE NETWORK DESIGN PROBLEM," EUROPEAN JOURNAL OF OPERATION RESEARCH, 79, 501-523, 1994.
[12]AYKIN TURGUT, "NETWORKING POLICIES FOR HUB-AND-SPOKE SYSTEMS WITH APPLICATION TO THE AIR TRANSPORTATION SYSTEM," TRANSPORTATION SCIENCE, 29(3), 201-221, 1995.
[13]AYKIN TURGUT AND GARY F. BROWN, "INTERACTING NEW FACILITIES AND LOCATION-ALLOCATION PROBLEM,"
TRANSPORTATION SCIENCE, 26(3), 212-221, 1992.
[14]BAHAR Y. KARA AND BARBAROS C. TANSEL, "ON THE SINGLE- ASSIGNMENT P-HUB CENTER PROBLEM " EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 125, 648-655, 2000.
[15]BANIA NEIL, PAUL W. BAUER AND THOMAS J. ZLATOPER, "US. AIR PASSENGER SERVICE: A TAXON -OMY OF ROUTE NETWORK, HUB LOCATION AND COMPETITION," TRANSPORTATION RESEARCH - E, 34( 1), 53-74, 1998.
[16]BOWEN JOHN, "AIRLINE HUBS IN SOUTHEAST ASIA: NATIONAL ECONOMIC DEVELOPMENT AND NODAL ACCESSIBILITY," JOURNAL OF TRANSPORT GEOGRAPHY, 8, 25-41, 2000.
[17]CAMPBELL JAMES F., "CONTINUOUS AND DISCRETE DEMAND HUB LOCATION PROBLEMS," TRANSPORTA -TION RESEARCH-B, 27B(6), 473-482, 1993.
[18]CAMPBELL JAMES F., "HUB LOCATION AND THE P-HUB MEDIAN PROBLEM," OPERATIONS RESEARCH, 44(6), 923-935, 1996.
[19]CAMPBELL JAMES F., "INTEGER PROGRAMMING FORMULATIONS OF DISCRETE HUB LOCATION PROBLEMS ,"
EUROPEAN JOURNAL OF OPERATION RESEARCH, 72, 387-405, 1994.
[20]CAMPBELL JAMES F., "LOCATION AND ALLOCATION FOR DISTRIBUTION SYSTEM WITH TRANSSHIPMENTS AND TRANSPORTATION ECONOMIES OF SCALE," ANNALS OF OPERATIONS RESEARCH, 40, 77-99, 1992.
[21]CAPTIVO M. EUGENIA, "FAST PRIMAL AND DUAL HEURISTICS FOR THE P-MEDIAN LOCATION PROBLEM ,"
EUROPEAN JOURNAL OF OPERATION RESEARCH, 52, 65-74, 1991.
[22]CHRYSSI MALANDRAKI AND ROBERT B. DIAL, "A RESTRICTED DYNAMIC PROGRAMMING HEURISTIC ALG -ORITHM FOR THE TIME DEPENDENT TRAVELING SALESMAN PROBLEM," EUROPEAN JOURNAL OF OPERAT -ION RESEARCH, 90, 45-55, 1996.
[23]CHUNG SUNG-HARK, YOUNG-SOO MYUNG AND DONG-WAN TCHA, "OPTIMAL DESIGN OF A DISTRIBUTED NETWORK WITH A TWO-LEVEL HIERARCHICAL STRUCTURE," EUROPEAN JOURNAL OF OPERATION RESEA -RCH, 62, 105-115, 1992.
[24]DASKIN MARK S. AND NICHOLAOS D. PANAYOTOPOULOS, "A LAGRANGIAN RELAXATION APPROACH TO ASSIGNING AIRCRAFT TO ROUTES IN HUB AND SPOKE NETWORK," TRANSPORTATION SCIENCE, 23(2), 91-95, 1989.
[25]DEBORAH L. BRYAN, "EXTENSION TO THE HUB LOCATION PROBLEM : FORMULATIONS AND NUMERICAL EXAMPLES," GEOGRAPHICAL ANALYSIS, 30(4), 315-330, 1998.
[26]DEBORAH L. BRYAN AND MORTON E. O'KELLY, "HUB-AND-SPOKE NETWORK IN AIR TRANSPORTATION : AN ANALYTICAL REVIEW," JOURNAL OF REGINAL SCIENCE, 39(2), 275-295, 1999.
[27]DENSHAM P. J. AND G. RUSHTON, "STRATEGIES FOR SOLVING LARGE LOCATION-ALLOCATION PROBLE -MS BY HEURISTICS METHODS," ENVIRONMENT AND PLANNING A, 24, 289-304, 1992.
[28]DENSHAM P. J. AND GERARD RUSHTON, "A MORE EFFICIENT HEURISTIC FOR SOLVING LARGE P-MEDI -AN PROBLEMS," PAPERS IN REGIONAL SCIENCE: THE JOURNAL OF RSAI, 71(3), 307-336, 1992.
[29]EBERY JAMIE, MOHAN KRISHNAMOORTHY , ANDREAS ERNST AND NATASHIA BOLAND, "THE CAPACITATE -D MULTIPLE ALLOCATION HUB LOCATION PROBLEM : FORMULATIONS AND ALGORITHMS," EUROPEAN JOURNAL OF OPERATION RESEARCH, 120, 614-631, 2000.
[30]FILHO V. J. M. F. AND R.D. GALVAO, "A TABU SEARCH HEURISTIC FOR THE CONCENTRATOR LOCAT -ION PROBLEM,"
LOCATION SCIENCE, 6, 189-209, 1998.
[31]GIOVANNI RIGHINI, "A DOUBLE ANNEALING ALGORITHM FOR DISCRETE LOCATION/ALLOCATION PROBL -EM,"
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 86, 452-468, 1995.
[32]GLOVER, F., "TABU SEARCH," PART I, ORSA JOURNAL ON COMPUTING, 1, 190-206, 1989.
[33]GOLDEN, B., "A STATISTICAL APPROACH TO THE TSP," NETWORKS, 7, 209-225, 1977.
[34]HASAN PIRKUL AND DAVID A. SCHILLING, "AN EFFICIENT PROCEDURE FOR DESIGNING SINGLE ALLO -CATION HUB AND SPOKE SYSTEM," MANAGEMENT SCIENCE, 44(12), 235-242, 1998.
[35]HOLMBERG KAJ, MIKAEL RONNQVIST AND DI YUAN, "AN EXACT ALGORITHM FOR THE CAPACITATED FACILITY LOCATION PROBLEM WITH SINGLE SOURCING," EUROPEAN JOURNAL OF OPERATIONAL RESEA -RCH, 113, 544-559, 1999.
[36]JINHYEON SOHN AND SUNGSOO PARK, "A LINEAR PROGRAM FOR THE TWO-HUB LOCATION PROBLEM," EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 100, 617-622, 1997.
[37]JINHYEON SOHN AND SUNGSOO PARK, "EFFICIENT SOLUTION PROCEDURE AND REDUCED SIZE FORMUL -ATIONS FOR P-HUB LOCATION PROBLEMS," EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 108, 118-126, 1998.
[38]KIRKPATRICK, S., C.D. GELATT. TR. AND M.P.VECCHI, "OPTIMIZATION BY SIMULATED ANNEALING ," SCI., 22, 671-680, 1983.
[39]KLINCEWICZ JOHN G., "A DUAL ALGORITHM FOR THE UNCAPACITATED HUB LOCATION PROBLEM," LOC -ATION SCIENCE, 4(3), 173-184, 1996.
[40]KLINCEWICZ JOHN G., "AVOIDING LOCAL OPTIMA IN THE P-HUB LOCATION PROBLEM USING TABU SEARCH AND GRASP," ANNALS OF OPERATIONS RESEARCH, 40, 283-302, 1992.
[41]KLINCEWICZ JOHN G., "HEURISTICS FOR THE P-HUB LOCATION PROBLEM," EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 53, 25-37, 1991.
[42]KLINCEWICZ JOHN G., "HUB LOCATION IN BACKBONE/ TRIBUTARY NETWORK DESIGN : A REVIEW," LOCATION SCIENCE, 6, 307-335, 1998.
[43]LEE YOUNGHO ,BYUNG HA LIM AND JUNE S.PARK, "A HUB LOCATION PROBLEM IN DESIGNING DIGIT -AL DATA SERVICE NETWORKS : LAGRANGIAN RELAXATION APPROACH," LOCATION SCIENCE, 4(3), 185-194, 1996.
[44]MARIANOV VLADIMIR, DANIEL SERRA AND CHARLES REVELLE, "LOCATION OF HUBS IN A COMPETITI -VE ENVIRONMENT," EUROPEAN JOURNAL OF OPERATION RESEARCH, 114, 363-371, 1999.
[45]MIRCHANDANI RITU B., AISSA OUDJIT AND RICHARD T. WONG, "MULTIDIMENSIONAL" EXTENSIONS AND A NESTED DUAL APPROACH FOR THE M-MEDIAN PROBLEM," EUROPEAN JOURNAL OF OPERATION RESEARCH, 21, 121-137, 1985.
[46]MUSTAHSAN MIR AND M. HASAN IMAM, "ANALYTIC ANNEALING FOR MACROCELL PLACEMENT OPTIMAL,"
COMPUTERS ELECT, 22(2), 169-177, 1996.
[47]O'KELLY MORTON E., "A QUADRATIC INTEGER PROBLEM FOR THE LOCATION OF INTERACTING HUB FACILITIES,"
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 32, 393-404, 1987.
[48]O'KELLY MORTON E., "A GEOGRAPHER'S ANALYSIS OF HUB-AND-SPOKE NETWORK," JOURNAL OF TRAN -SPORT GEOGRAPHY, 6(3), 171-186, 1998.
[49]O'KELLY MORTON E., "HUB FACILITY WITH FIXED COSTS," PAPERS IN REGIONAL SCIENCE: THE JOURNAL OF RSAI, 71(3), 293-306, 1992.
[50]O'KELLY MORTON E., "THE LOCATION OF INTERACTING HUB FACILITIES," TRANSPORTATION SCIEN -CE, 20(2), 92-105, 1986.
[51]O'KELLY MORTON E., DARKO SKORIN-KAPOV AND JADRANKA SKORIN-KAPOV, "HUB NETWORK DESIGN WITH SINGLE AND MULTIPLE ALLOCATION A COMPUTATIONAL STUDY," LOCATION SCIENCE, 4(3), 125-138, 1996.
[52]O'KELLY MORTON E., DARKO SKORIN-KAPOV AND JADRANKA SKORIN-KAPOV, "LOWER BOUNDS FOR THE HUB LOCATION PROBLEM," MANAGEMANT SCIENCE, 41(4), 713-721, 1995.
[53]O'KELLY MORTON E. AND D. L. BRYAN, "HUB LOCATION WITH FLOW ECONOMIES OF SCALE," TRANSP -ORTATION SCIENCE - B, 32(8), 605-616, 1998.
[54]O'KELLY MORTON E. AND YUNG LAO, "MADE CHOICE IN A HUB-AND-SPOKE NETWORK : A ZERO-ONE LINER PROGRAMMING APPROACH," GEOGRAPHICAL ANALYSIS, 23(4), 283-297, 1991.
[55]RICKLEFS JOHN AND CHIA-JUCH CHANG, "TAIWAN'S HUB PORT POLICY UNDERSTANDING TAIWAN'S POSITION IN THE FUTURE LANDSCAPE OF CENTRAL ASIA," TRANSPORTATION PLANNING JOURNAL, 22 (4), 479-492, 1993.
[56]ROLLAND ERIK, DAVID A. SCHILLING AND JOHN R. CURRENT, "AN EFFICIENT TABU SEARCH PROCE -DURE FOR THE P-MEDIAM PROBLEM," EUROPEAN JOURNAL OF OPERATION RESEARCH, 96, 329-342, 1996.
[57]SASAKI MIHIRO, ATSUO SUZUKI AND ZVI DREZNER, "ON THE SELECTION OF RELAY POINTS IN A LOGISTICS SYSTEM," ASIA-PACIFIC JOURNAL OF OPERATION RESEARCH, 14, 39-54, 1997.
[58]SASAKI MIHIRO, ATSUO SUZUKI AND ZVI DREZNER, "ON THE SELECTION OF HUB AIRPORTS FOR AN AIRLINE HUB-AND-SPOKE SYSTEM," COMPUTERS & OPERATIONS RESEARCH, 26, 1411-1422, 1999.
[59]SKORIN-KAPOV DARKO AND JADRANKA SKORIN-KAPOV, "ON TABU SEARCH FOR THE LOCATION OF INTE -RACTING HUB FACILITIES," EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 73, 502-509, 1994.
[60]SKORIN-KAPOV DARKO, JADRANKA SKORIN-KAPOV, AND MORTON O'KELLY, "TIGHT LINEAR PROGRAMMI -NG RELAXATIONS OF UNCAPACITATED P-HUB MEDIAN PROBLEM," EUROPEAN JOURNAL OF OPERATIONA -L RESEARCH, 94, 582-593, 1996.
[61]TAICHI KAJI AND AZUMA OHUCHI, "A SIMULATED ANNEALING ALGORITHM WITH THE RANDOM COMPOUN -D MOVE FOR THE SEQUENTIAL PARTITIONING PROBLEM OF DIRECTED ACYCLIC GRAPHS," EUROPEAN JOURNAL OF
OPERATIONAL RESEARCH, 112, 147-157, 1999.
